tan(45° + θ) · tan(45° − θ) is equal to:
A(1 + tan²θ) / (1 − tan²θ)
B(1 − tan θ) / (1 + tan θ)
Ctan 2θ
D1
Answer & Solution
Correct answer: D. 1
1. tan(45° + θ) = (1 + tan θ) / (1 − tan θ); tan(45° − θ) = (1 − tan θ) / (1 + tan θ).
2. Multiplying them: [(1+tanθ)/(1−tanθ)] · [(1−tanθ)/(1+tanθ)] = 1.
3. So the product equals 1 for any θ where both tans are defined.
_Source: NCERT Class 11 Maths Ch 3 §3.4 Trig Identities_
Related questions
If cos θ = −1/2 and θ ∈ (π, 3π/2), then θ equals:sin 75° equals:By the law of sines in a triangle, a / sin A is equal to:The general solution of cos x = 0 is:The general solution of sin x = 0 is:If sin θ = 3/5 and θ is acute, then cos θ equals:The angle in radians for 120° is:The principal value of the range of f(x) = sin x is: